Lyapunov's First Theorem

A necessary and sufficient condition for all the eigenvalues of a real n×n matrix A to have negative real parts is that the equation


has as a solution where V is an n×n matrix and (x,Vx) is a positive definite quadratic form.

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Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1122, 2000.

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Lyapunov's First Theorem

Cite this as:

Weisstein, Eric W. "Lyapunov's First Theorem." From MathWorld--A Wolfram Web Resource.

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